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3 years ago

Solve the system of equations 5x – 2y = 19 and -x + y = 1 by combining the equations.

Mathematics

1 answer:

Zarrin [17]3 years ago

3 0

Answer:

Step-by-step explanation:

5x - 2y = 19

-5x + 5y = 5

3y = 24

y = 8

-x + 8 = 1

-x = -7

x = 7

(7, 9)

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Find the dimensions of the rectangular corral producing the greatest enclosed area given 320 feet of fencing. (Assume that the l

jenyasd209 [6]

Answer:

The dimensions of the rectangular corral producing the greatest enclosed area is a square of 80 ft x 80 ft

Step-by-step explanation:

Let

x -----> the length of the rectangular corral in feet

y -----> the width of the rectangular corral in feet

we know that

The area of the rectangular corral is equal to

$A=xy$ -----> equation A

The perimeter of the rectangular corral is equal to

$P=2(x+y)$

$P=320\ ft$

$320=2(x+y)$

Simplify

$160=(x+y)$

$y=160-x$ -----> equation B

substitute equation B in equation A

$A=x(160-x)$

$A=-x^2+160x$

This is a vertical parabola open downward

The vertex is a maximum

The x-coordinate of the vertex represent the length for the maximum area

The y-coordinate of the vertex represent the maximum area

Convert the quadratic equation in vertex form

$A=-x^2+160x$

Factor -1

$A=-(x^2-160x)$

Complete the square

$A=-(x^2-160x+80^2)+80^2$

$A=-(x^2-160x+80^2)+6,400$

Rewrite as perfect squares

$A=-(x-80)^2+6,400$

The vertex is the point (80,6,400)

$x=80\ ft$

The maximum area is 6,400 ft^2

<em>Find the value of y</em>

$y=160-x$ ----> $y=160-80=80\ ft$

therefore

The dimensions of the rectangular corral producing the greatest enclosed area is a square of 80 ft x 80 ft

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3 years ago

Imagine you are the Ghost of Pheidippides. Write the whole story of the Battle of Marathon from your point of view.

Lapatulllka [165]

Answer:

Understand the question and solve it

Step-by-step explanation:

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2 years ago

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Inessa05 [86]

You used distributive property because when there’s parentheses in a equation you need to distribute the number outside of the parentheses

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3 years ago

How would you integrate (2x-1)(6x+5)? is there a product rule for integration?

NikAS [45]

No, there is not a product rule for integration.

To integrate (2x - 1)(6x + 5), start expanding the product:

(2x - 1)(6x + 5) = 12x^2 + 10x - 6x - 5 = 12x^2 + 4x - 5.

Now, I guess you know how to integrate that:

∫ (12x^2 + 4x - 5) dx = ∫12x^2 dx + ∫4x dx + ∫ (-5) dx = 4x^3 + 2x^2 - 5x + C

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3 years ago

A recipe that yields 2 loaves of bread

kozerog [31]

Answer:He can make 7.5 loaves i think

Step-by-step explanation:

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2 years ago